Month: March 2012

Total 10 Posts

Five Design Patterns for Digital Math Curricula

The Center for the Study of Mathematics Curriculum invited me to give a talk last week on digital math curricula. I described how print curricula limit the experiences we can offer our math students and then I made five recommendations for designing experiences digitally:

  1. Show, don’t tell.
  2. Introduce the task as early and concisely as possible.
  3. Climb the entire ladder of abstraction.
  4. Crowdsource patterns.
  5. Prove math works.

Any questions or criticism, please don’t hold back in the comments. I also have limited availability for consultation on these kinds of projects. Drop me a line at

2012 May 1. Here’s the feedback [pdf] from the academics at the conference.

101questions: Behind The Scenes

[cross-posted to the 101questions blog]

We’re one week into 101questions and the early feedback has been encouraging. For a certain kind of warped individual (ie. my kind of individual) the experience seems to be, in a word, addicting. It’s also fun to find a non-trivial Swedish contingency jumping aboard. The more effective use we make of visuals, the more we can include learners who speak English as a second language, if they speak it at all.

After a week, 500+ registered users have uploaded 300+ photos and videos which have provoked 10,000+ questions across all users, including a number of unregistered users I haven’t counted. (The analytic component of site administration is right in my wheelhouse, as you can see.) We even have a registered troll, which means we’re halfway to a full-fledged online community.

Here’s a description of where 101questions came from, the problems it tries to solve, and a few notes on where it might go.

Where It Came From

I piloted the idea online in webinars and face-to-face in workshops. I tweaked the constraints and the implementation and arrived at an exercise that teachers found both challenging and fun, which seemed like the right combination. Teachers liked rating photos and videos as perplexing (or not). That same feedback on their own photos and videos helped them improve their eye for perplexity.

I introduced it on Twitter as #anyqs. You’d post a link to a photo or video (hereafter called “the first act”) and ask for questions. That implementation was good for a time, but ultimately very problematic.

Problems 101questions Tries To Solve, In Order Of Importance

Here’s the biggest:

The feedback to your first act is proportional to the quantity of your Twitter followers.

yeah, well that works great with almost 7500 followers. Less well with 4. That arent math teachers.

I have the most followers of anyone who has contributed to the #anyqs tag. I also get the most responses to my photos and videos. That correlation extends all the way down to people with a dozen followers who get very few responses in spite of their work being thoroughly perplexing. That’s a pity.

At 101questions, your first act goes into a huge pile along with mine and both of ours are served up randomly to other users until it gets 100 responses.

People post whatever they want and tag it #anyqs.

I’m talking about full web pages, long, meandering videos, Flash applets, etc. There is a place for all those things, but they all miss the design of the exercise: one photo or one minute of video.

At 101questions, your attempt to upload anything outside of those constraints will get you an invitation to revise and resubmit.

Tweets are fleeting. Perplexity should endure.

We don’t have a record of all the perplexing photos and videos you’ve posted on Twitter. Many of the #anyqs participants likely couldn’t dredge up their own contributions. I’ve saved all of them locally, but that takes a lot of diligence and they’re basically lost to the wind for everybody else. Along those lines, it’s also hard to know if someone has already posted a particular first act.

At 101questions, your contributions are stored in a database and logged in your profile. (Here’s mine.) The application also checks to see if a particular link has already been uploaded and, if so, points you to it. There is a bookmarking feature. You can save first acts for later.

It’s hard to know if you’re bored by my first act or if I just missed you.

I wish there were a “Skip It, I’m Bored” button attached to my #anyqs submissions on Twitter. If responses to my first act are light, I may infer it wasn’t perplexing, but sometimes I wonder if I just queried my followers at the wrong time.

At 101questions, there is a “Skip It, I’m Bored” button.

There isn’t any way to filter for quality.

What was the best photo posted last month? Which people post the best material most consistently? Where can I find their photos and videos? How are we defining “best” anyway? Those questions can’t be answered within our Twitter pilot.

At 101questions, I’ve set up a metric called “perplexity” which amounts to the likelihood your first act will provoke a question. (Technically, it’s the number of questions that have been asked about your first act expressed as a percentage of total skips and questions. 75 means three quarters of everybody who has seen your first act have asked a question about it.)

People post material because it seems vaguely connected to a discipline, not because it provokes a question.

“Interesting” isn’t the same as “perplexing.” “Engaging” is a different animal also. It’s easier to dazzle a student with fireworks than to provoke her to wonder a question. When I’m unperplexed by someone’s #anyqs material on Twitter, I’ll often tweet back, “What question did that photo make you wonder?” In my perfect world, I’d see your own question alongside the first act you uploaded, but only after I submitted my own, so my question is raw and unbiased by yours.

At 101questions, the upload page has fields for a link and a title. Then a blank for your question.

It’s difficult to see other people’s questions about a first act.

If someone tweets a first act I find perplexing, I often want to know if it perplexed other people and, if it did, the questions they asked. That’s difficult on Twitter.

At 101questions, everyone’s questions are logged beneath each first act.

Where This Might Go

Tagging. Searching. Commenting. Top ten lists for “today” and “the last week,” not just “all time.” A mobile application. The ability to submit files from your phone or computer, not just links. Complete mathematical stories, not just the first act. If we’re working on circumference tomorrow, I’d like to go to 101questions, find a list of complete mathematical stories for “circumference” sorted from most perplexing to least, and then download it to my hard drive. Those features will be expensive to develop and sustain. The core feature – getting 100 responses to your first act – will always be free but I may invite you to pay community membership dues for access to the fancier stuff.

Way, Way Behind The Scenes

One of the most annoying features of edu-punditry is how quickly our gurus decide they’ve done absolute everything they can to help us understand and accomplish their vision for learning. They write their blogs, publish their books, tweet their tweets, and give their speeches. Having decided they’ve done everything possible to help us wrap our brains around ideas that are obvious to them, their last recourse is to snark, sarcasm, hectoring, and irrelevancy.

In reality, their messages can almost always be clarified, made easier, more fun, and less expensive. I want nothing to do with that culture of punditry. I can be clearer. I can find new metaphors. I can publish in more media. And I can create tools to make these practices easier. That’s 101questions.

Vi Hart v. Sal Khan

Timon Piccini mashes up one of Sal Khan’s lectures with one of Vi Hart’s indictments of lectures and the result is difficult to watch:

Of course, Khan went on to hire Hart, a partnership which could be yielding all kinds of fruit. If anybody has noticed Khan innovating on his format since he picked up Hart, drop me a line in the comments.

Featured Comment

Mr. Bombastic:

The KA lectures may or may not be effective in helping people with math, depending on your idea of “helping”. The KA problem sets are almost certainly going to give many students the impression that they know and understand something that they do not. Naive teachers may be taken for a walk along this primrose path as well. For that reason I think the problem sets could be quite destructive. I don’t object to checking for mastery, but KA doesn’t even come close to having assessments that measure mastery.

2012 Mar 24. James C. points out this collaboration.


Let me invite you to check out 101questions, a website I’ve been building since last fall.

Other websites will let you “like” something or call it a “favorite” or “interesting” or give it a thumbs up or a +1. As a teacher, I don’t aspire to any of those things as much I aspire to be perplexing. I want to perplex my students, to put them in a position to wonder a question so intensely they’ll commit to the hard work of getting an answer, whether that’s through modeling, experimenting, reading, taking notes, or listening to an explanation.

A lot of my most perplexing classroom moments have had two elements in common:

  1. A visual. A picture or a (short) video.
  2. A concise question. One that feels natural. One that people can approach first on a gut level, using their intuition.

Let’s call that a first act. There are still two more acts and a lot of work yet to do, but the first act is above and before everything else.

It’s been difficult for me to know in advance whether or not my first acts will perplex my students. Sometimes they confuse my students. Sometimes the warped lens I have on the world indicates something perplexing but it bores my students. For awhile I inoculated myself against that possibility by tossing the photo out to my Twitter followers and asking them “Any questions?

Their responses have been extremely helpful, but limited in some ways that 101questions will fix. I’ll describe those in more detail in another post.

For now, check it out. Ask some questions. Upload a first act. Wait for the questions (or skips) to roll in. Then figure out how you’ll help your students get answers.

I Would Have Loved Khan Academy In Eighth Grade

Not to make my my position overly complicated, but I would have loved Khan Academy as an eighth grader, when I was first learning algebra.

My twin sister and I were homeschooled up until ninth grade when the difficulty of math outstripped my mom’s ability to teach it to us. So we ordered a stack of VHS tapes featuring Leonard Firebaugh and his whiteboard. I can’t believe I’ve never connected his videos to Khan Academy until now.

Those videos were boring but I was grateful for them because the alternative was nothing. So let me say that I completely understand the enthusiasm you’ll find from homeschool parents in the comment threads of any given report on Khan Academy. (The religious homeschoolers offer Khan their prayers in addition to their thanks, and I understand that too.) When Mark Halberstadt thanks Khan for helping him clear hurdles to study electrical engineering at Temple, I don’t have anything in me except gratitude for the fact that something existed for Halberstadt where once there was very little.

I was grateful for Leonard Firebaugh because the alternative was nothing. But better than nothing and better than Leonard Firebaugh were the classrooms of Messrs. Selim, Cavendar, Bishop, and Whipkey, where we did math more than any one person talked about it, where I had to unlearn and relearn a lot of Algebra I thought I had mastered. You couldn’t combine the two. You couldn’t pause the doing of mathematics and then turn us over to watching someone else do mathematics for upwards of ten to twenty minutes. It would have been a collision of two hostile worlds.