It’s the muscle that connects my capacity for noticing the world to my capacity for creating mathematical experiences for children. (I should also take some time in 2018 to learn how muscles work.)

By way of illustration, this was my favorite tweet of 2017.

Gathering some data re: perfect banana ripeness. Have 5 seconds? Fill out a one-question survey! https://t.co/r9UQA1RlC6 #mathchat #MTBoS pic.twitter.com/BrYtUpfa7h

— Ilona Vashchyshyn (@vaslona) September 29, 2017

Right there you have an image created by Brittany Wright, a chef, and shared with the 200,000 people who follow her on Instagram. Loads of people before Ilona had noticed it, but she connected that noticing to her capacity for creating mathematical experiences for children. She surveyed her Twitter followers, asking them to name their favorite banana, receiving over one thousand responses. Then on her blog she posed all kinds of avenues for her students’ investigation — distributions, probability, survey design, factor analysis, etc.

That skill — taking an interesting thing and turning it into a challenging thing — is one of teaching’s “unnatural acts.” Who does that? Not civilians. Teachers do. And I want to get awesome at it.

But Ilona ran a marathon and I want to run some wind sprints. I need quick exercises for strengthening that muscle. So here are my exercises for 2018:

I’m going to pause when I notice mathematical structures in the world. Like flying out of the United terminal in San Antonio at last year’s NCTM where I (and I’m sure a bunch of other math teachers) noticed this “Suitcase Circle.”

Then I’ll capture my question in a picture or a video. Kind of like the one above, except pictures like that one exist in abundance online.

Civilians capture scenes in order to preserve as much information as possible. That’s natural. But I’ll excerpt the scene, removing some information in order to provoke curiosity. Perhaps this photo, which makes me wonder, “How many suitcases are there?”

In order to gauge the curiosity potential of the image, I’ll share the media I captured with my community. Maybe with my question attached, like Ilona did. Maybe without a question so I can see the interesting questions other people wonder. You may find my photos on Twitter. You may find them at my pet website, 101questions.

I want to get to a place where that muscle is so strong that I’m hyper-observant of math in the world around me, and turning those observations into curious mathematical experiences for children is like a reflexive twitch.

(Plus, that muscle will be more fun to strengthen in 2018 than literally any other muscle in my body.)

BTW. Check out the 3-Act Task I created for the Suitcase Circle. It includes the following reveal, which I’m pretty proud of.

BTW. The suitcase circle later turned into Complete the Arch, a Desmos activity, which has some really nice math going on.

[Suitcase Circle photo by Scott Ball]

Featured Comment

Ilona Vashchyshyn :

I would just add that we shouldn’t forget that the classroom is a world within a world for us to notice, and that while many great, unforgettable tasks are based on interesting phenomena that we’ve observed or collected outside of school, on a day-to-day basis, high-impact tasks are probably more likely to be rooted in our observations and interactions with our students (in fact, even the banana tweet and post were sparked by a conversation with a student who was eating what was, to me, an exceptionally green banana). They tend not to be as flashy, but can have just as much impact because they’re tailored to the kids, norms, relationships, and histories in our classrooms.

My mother made me a scientist without ever intending to. Every other Jewish mother in Brooklyn would ask her child after school: So? Did you learn anything today? But not my mother. “Izzy,” she would say, “did you ask a good question today?” That difference – asking good questions – made me become a scientist.

The big changes:

• You can upload files now. No more pasting links to external content. You no longer have to upload your image to Dropbox or ImageShack or anywhere else (an incredibly cumbersome step for a lot of people) just to get material onto 101questions. We’re no longer restricted to YouTube’s hardline interpretation of Fair Use either.
• You can download files now. Click “Actions” on any uploaded first act and then click “Download.” It’s awesome. It downloads whatever file the user uploaded (it won’t pull down content uploaded to YouTube or Vimeo) along with a text file with all the submitted questions.
• You can get more responses more quickly by sending your link around. It bummed people out that they’d link to a first act and other people couldn’t add a question unless they saw it randomly come up on the homepage. “You should be able to add a question to the page itself,” they said. I resisted but I was wrong and now you can.

The small changes:

• A pile of corrections to aspects of the UI that annoyed me, Amazon S3 integration, automatic comment subscription, a lot ground laid for the winter update.

Here are the top-level updates for 101questions:

1. You have better quality control rankings. I’m no longer listing the top ten most perplexing people on the site. We can bring that list back if we miss it, but my sense from conversations on this blog and at Stanford is that it was ultimately more divisive than useful. I’ve also split the top ten lists for photos and videos and added a “right now” option alongside the “all time” rankings, so we can see what’s recently perplexing.
2. You can bookmark questions now. Maybe your first act received eighty questions, but those eighty questions are really only composed of four or five distinct questions. You can now click a bookmark icon and put them in order from most common to least. You’ll help other people (and yourself) get a better sense of the questions people asked about your first act. (See what I mean with US Bank.)
3. Comments. You asked for comments. You got ’em.
4. You can delete your own first acts now. Maybe someone’s comment gave you a better idea for your timelapse video of grass growing on your lawn. Now you can delete the old one before you upload the new one.
5. You have better access to the feedback on all your first acts. I’m really happy with the new “latest” tab in your profile. It has more information – you’ll see questions and skips like before but also comments and bookmarks – in a cleaner layout.
6. You won’t be able to upload itty-bitty images anymore. The uploader makes sure your pictures are at least the size of the viewing window.
7. I got rid of Facebook, Twitter, and G+ sharing. No one used them and Twitter uses them to stalk you around the web. So I got rid of them and replaced them with a “Copy Link” option that puts the shortlink on your clipboard. You decide what you want to do with it.
8. Animated GIFs are now supported.
9. You can search the site. Something that’s a little fun is that even though you haven’t tagged your first acts in any particular way, other users have. They’re asking questions about your photos and videos and our search engine finds in those questions the semantic goodness it craves. (ie. “Everyone is asking questions about a basketball?” says our genial and dimwitted search engine. “Maybe this first act is about a basketball!”) I’ll be messing with the algorithm over time but ideally, at some point in the near future, you’ll come to the site saying to yourself, “I’d love to motivate completing the square with a video of Australian rugby” (or something equally unlikely) and the site will deliver.

Add in a slew of of performance tweaks and other odds and ends and you have a site update that’s been a long time in the making. If you see anything fun or funny, don’t hesitate to let me know.

1. San Francisco House, Scott Farrar.
2. Costco TV, Megan Hayes-Golding.
3. Bill Roll, Joe Kremer.
4. Good Tip / Bad Tip, Joe.
5. Little Boy Counting, David Wees.

My Own Listing:

• Mini-Bagels

Data Dump:

I’m obliged to Phil Wagner for helping me parse 30,000+ questions:

Most Common First Word

49%: How
18%: What
5%: Is
4%: Why
3%: Which

Most Common First Two Words

20%: How many
10%: What is
10%: How much
6%: How long
2%: How big

Most Common First Three Words

8%: What is the
2%: How long will
1%: What are the
1%: How big is
1%: How many people

Most Common First Four Words

2%: How long will it
1%: How big is the
1%: How tall is the
1%: How long is the
1%: How long does it

1. How useful is 101questions as a proxy for student interest?
2. For example, when we find that 19% of 101questions users skip The Ticket Roll, does that mean that 19% of math students will skip it also?
3. When we scribble information all over our images in our textbooks (instead of presenting concrete contexts) how does that affect their perplexity?
4. For which contexts is video useful? Is the Pyramid of Pennies more perplexing as a photo or a video?
5. Does a tripod matter? How is a student’s interest in a video affected if it features a slight wiggle rather than if the camera is locked down?

Niche questions, certainly, but they interest me so I set up two installations of the 101questions software at eagle.101qs.com and hawk.101qs.com to answer them.

What You Can Do For Me

If you are in a 1:1 classroom where Vimeo and YouTube aren’t blocked, and you have twenty free minutes between now and the end of the year, you can help me answer them.

In the comments, let me know how many students you can commit and in what classes. I’ll e-mail you a handout (looks like this) you can cut up and pass out to your students.

The rest should be smooth. Once the number of conscripted students clears a certain bar, I’ll close the thread.

BTW: Nathan Kraft surveyed his students along similar lines. The results are fascinating.

2012 May 30: That’ll do it. Comments closed. Thanks for your help, everybody.

• Doggie Bandana, Marshall Thompson. Marshall got me good with this one.
• Water Power Plant, Bernard. Similar to Windmill. In both cases, I’d like to know if what we’re seeing would power a light bulb, a fridge, or a car. As in, I really want to know. No math teacherly pretense here. If you can help me answer that question, I am your eager student.
• Snow, man, Patrick Brandt. I skipped this one initially, but Patrick’s question has been gnawing at me since I saw it. Can anyone suggest a redesign?
• London Eye, Edwin Ulmer. I’ve been looking for just this kind of clip for a long while. Three cheers for Internet-based collaboration.
• Shoot the Gap, LDH. Recently, I expressed a sense that posting video of GGB / GSP applets tends to miss the best parts of both. This one is different.

My own listings:

• Coffee Traveler
• Popcorn Picker

At the end of a session in Toronto just now somebody asked me how much time it takes to come up with these kinds of tasks. “More or less than when you made tasks on paper?”

“Definitely more,” I said. But, brother, can you see I’m trying to suppress some kind of goofy smile in Popcorn Picker? Same with Coffee Traveler, where I’m grinning off screen. At a certain point, I stopped coding this kind of production as “work.” No disrespect at all if that’s not your thing.

Data Dump:

Do people who upload more have higher perplexity scores? No, they don’t. I would like to see an animation of those points over time, though.

Am I imagining it, or are the participants (posters and respondents) mostly male? I’d love to be wrong about this. If I’m not wrong, then why would that be the case? And more importantly, has anyone noticed whether there is there any difference in class participation between female and male students when these are used in class?

I don’t ask for your gender during the registration process so it’s hard for me bring any data to bear on the question. But if I allow myself some conservative guesses, it seems that at the time of this writing:

1. the top ten most perplexing users are all male,
2. nine of the top ten most perplexing first acts were uploaded by males.

So help me, I can’t figure out how the interaction on the site (ask a question and click “skip”) or the nature of the tasks (a context and a question) preferences men. The reviews are all blind, too. I’m looking at a photo. Maybe it was uploaded by Candice Director. Or maybe by Dan Anderson. It’s impossible to know until later.

I’m highlighting Elizabeth’s comment to see if anyone can help me figure this out. I’d rather this didn’t turn into a general complaint window, though. I’m interested in locating the source of any gender bias, not in airing out any other grievances.

BTW: My adviser has done a lot of work in gender and math. I should probably check in.

Featured Comment:

Too many. A really great discussion down below. Here’s a link to my summary.

• Circle or Polygon? Scott Farrar. This thing is poised to take over the all-time list once it crosses the 25-response threshold.
• Lemonade, Christopher Danielson. On some other site – let’s call it Bizarro 101questions – Danielson uploaded a video in which he dropped a can of concentrate into each of those containers and started filling them with water.
• Megalodon Tooth, Jake Jouppi. I know I declared a moratorium on this kind of imagery (which is all over the site at this point) but think about the size of that shark, okay?
• Ping Pong, Bob Lochel. Great first act with strong implications for the third.
• Roller Coaster Steepness, Tom Ward. An excellent supercut of roller coasters that asks the student to first decide which one feels steepest (that’s a low rung on the ladder of abstraction) before using mathematical analysis to determine which one actually is steepest.

My own listings:

• Amgen Race
• Pocket Change

Data Dump:

Median photo perplexity: 46.
Median video perplexity: 51.

Photos own the top ten list but videos are more perplexing, on balance.

An embarrassment of riches this week. It was difficult keeping this to five:

• Too good to be true, Scott Keltner. So is it … free … then? I give this image strong odds on provoking a class debate and highlighting some of your students’ misconceptions of percent growth.
• Car Chase, Ryan Brown. The current darling of 101questions. (12 questions, no skips, as of this writing.) Notice how the first car smacks into the second, which was hidden off-screen. That’s stylish camera work!
• Muggsy Bogues, Tony Gumbo. The question, “How much shorter is Muggsy Bogues?” is one thing. “How many different ways can you express that difference?” is another. (eg. Absolute v. relative.) Start with the first. End with the second.
• First day of school, John Golden. “Is your height linear?” It’s a striking visual and the units along the “x-axis” are identical so you have a rare moment to examine the growth of height over time using people in photographs rather than points on a graph.
• Plinko, Michael Pershan. Yeah, great cut at the end there. Where’s the wisdom in putting the biggest pay-out beneath the most likely bucket? Bowen? (Related: this image, taken from this video.)

Other notes:

• Counting is so last winter. You’ll notice that your first ten responses will generally come from the same ten-or-so people who have seen everything uploaded to 101questions and keep current on all new uploads. It’s interesting to watch their tastes change. For instance, counting lots of little things used to be a lot of fun for this crowd, but now, as Tony Gumbo’s Bryant Denny Stadium can attest, counting is out. (Which isn’t to say that rating won’t pick up once more casual users check in, just that the obsessives have made their decision about counting.)
• Speaking of obsessives, Andrew Stadel has written a great tutorial for getting the most out of 101questions.
• Veggie Juice swings for the fences. You decide where it lands.
• Closing. Timon Piccini’s Cab Ride is the first first act to “close,” which means 100 people responded to it. Now it goes to the very bottom of the pile on the homepage, where it’ll only be seen once people have seen everything else. Initially, I thought first acts would close in a matter of hours after being uploaded. That was naive. It took months.

Plus my own listing:

• Edmonton Water Consumption, uploaded on a dare from Sean Geraghty. My assumption is it’s going to get clobbered.

Featured Comment

Ryan Brown:

At this point, I’ve posted about 300 questions. I’ve noticed that I’ve kind of changed my approach for coming up with questions for other people’s items. Rather than try to guess the question that fits as math teacher, I’m trying to put myself in the shoes of a 9th grader and decide “will they find this perplexing”? Fuzzy pictures: skip. Small font items like receipts and print advertisements that are full of numbers and words but no overtly visual content: skip. I’m also noticing that I’m beginning to skip items that are repeats of previously seen items — even just same genre items like super large ________. Initially, the questions were leaping right out at me. But now I feel like the student who says “oh, we’re doing this again.” No longer perplexed if I know what the teacher wants me to say. (Full disclosure: 2 of my 7 uploads are “world’s largest ______” related). Am I too harsh here, or are other people taking a similar approach?

I’m also finding a difference between “perplexing” and “interesting”. There’s a ton of stuff out there that is very cool and very interesting (intricate artwork, geometric designs, etc), but there is no obvious solvable mathematical question that is just begging to be asked. I skip those every time.