Get Posts by E-mail

2015 Remainders

Let’s close out 2015. In this remainders edition:

  • Eight new blog subscriptions from November & December.
  • Five essential 2015 posts from this blog.
  • Three bloggers I envy.
  • Seventeen Great Classroom Action posts I never got around to posting.


  • We successfully goaded Brett Gilland into tweeting and blogging. His writing features art, wit, and insight for days. Best follow of my fall quarter.
  • Jason D’Arcangelo is an elementary math coach, making him rare company online.
  • Kendra Lomax does interesting work in elementary math education also, most recently with the University of Washington’s Teacher Education by Design project.
  • Damian Watson just came off a two-year blogging hiatus with a post featuring Malcolm Swan, Andrew Stadel, and cognitive conflict, which pushes all three of my buttons.
  • Meryl Polak likewise came off a maternity leave to post about her experience designing and implementing a 3 Act Math task.
  • Geoff Wake was one of my colleagues at the Shell Centre when I set up a tent in their offices several years ago. Great guy. Interesting thinker. I’m excited to see him maintaining a blog.
  • Jenn Vadnais does consistently interesting work with the Desmos Activity Builder. I’m tuned in, hoping to learn how she works.
  • Glen Lewis blogs thoughtfully about technology, learning, and engagement in math education.

These blogs are each low volume, producing maybe one post per month. There is zero risk of getting overwhelmed here. Just toss them in Feedly or some other RSS reader and enjoy their insight whenever they find the time to share it.

Honorable Mentions

I don’t have a lot of envy in me for other Internet math ed types – their followers, retweets, subscribers, etc. Just keep working. What does turn me green, what I do covet, though, is another blogger’s ability to stir up conversation, to mobilize and collect the intellect of his or her readers. In 2015, that was Dylan Kane, the blogger whose posts invariably had me clicking through to the comments to see what he managed to provoke from his readers, then scratching my head trying to figure out how he did it.

If your heart belongs to elementary math education, the best moderators I have found there are Tracy Zager and Joe Schwartz.

My Year in Review

If you’ve come to this blog only recently, here are five posts that received a lot of traffic and commentary this year:

Looking for favorites from the wider online math education community? Check out the #MTBOS2015 hashtag. If I had to award my own MVP, it’d be Elizabeth Statmore’s “How People Learn” and how people learn where she turns essential research into manageable practice.

Great Classroom Action

And now, shamefully presented without commentary, seventeen posts I read in 2015 that had me check myself and think, “That classroom action is great!” I haven’t shared these yet and it’s time to clean the cabinet.


The New York Times looks at the dismal testimony of an “accident reconstructionist”:

The “expert witness” in this case would not answer questions without his “formula sheets,” which were computer models used to reconstruct accidents. When asked to back up his work with basic calculations, he deflected, repeatedly derailing the proceedings.

Watch the video. It’s well worth your time and I promise you’ll see it in somebody’s professional development or conference session soon. It offers so much to so many.

And then help us all understand what went wrong here. What’s your theory? Does your theory explain this catastrophe? Does it recommend a course of action? If you could go back in time and drop down next to this expert as he was learning how to make and analyze scale drawings, how would you intervene?

My own answer starts off the comments.

BTW. Can anyone help us understand how the expert came to the incorrect answer of 68 feet?

BTW. Hot fire:

The motorcyclist’s lawyer filed a counter-motion to refuse payment to the expert witness. It contained the math standards for Wichita middle schools.

[via Christopher D. Long]

2016 Jan 2. The post hit the top of Hacker News overnight.

2016 Jan 2. One of the Hacker News commenters notes that the actual deposition video is available on YouTube.

Featured Comments:

gasstationwithoutpumps offers one explanation of the error:

3 3/8″ at a 240:1 scale gives 67.5′ which rounds to 68′

It is easy to mix up 3/8″ and 3/16″, which is one reason I prefer doing measurements in metric units.

katenerdypoo offers another:

It’s quite possible he accidentally keyed in 6/16, which when multiplied by 20 gives 7.5, therefore giving 68 feet. This is also a reasonable error, since the 6 is directly above the 3 on the calculator.

Jo illustrates a fourth grader’s process of solving the scale problem.

Robert Kaplinsky chalks this up to pride:

Lastly, it’s worth noting that eventually the heated conversation shifts from the actual math to whether or not he will do it or can do it. At that point it seems to become a pride issue.

Alex blames those awful office calculators:

The reconstructionist is given an office calculator, which doesn’t even have brackets. He needs to enter a counter-intuitive sequence of “3/16+3” to even get the starting point. When I was at school I remember being aware that most people wouldn’t be able to handle that kind of mental contortion. They’d never been asked to.
So what’s the problem, and how might we solve it? Well, the man’s been given the wrong tool for the job. He’s never been asked to use the wrong tool before & so this throws him. This makes him defensive and he latches onto an excuse about formula sheets.

Jeff Nielso:

The motorcyclist’s lawyer is the unrelenting classroom didactic whose motivation is based on making his student look and feel stupid. I was waiting for Act 2 where the lawyer would jump up, grab his felt marker, and demonstrate just how easy he can show the procedure.


Interesting note: my grade 7 math class is in the middle of our unit on fractions, decimals, and percents, so I showed them this video so we could work on the problem. I thought they’d get a chuckle out of it and feel good about solving a problem that the expert on TV couldn’t solve.

Their reaction was unanimous. They identified with the guy and wanted them to give him his formula sheets. Some of them were pretty riled up about it!

They’re quite accustomed to me showing them videos and doing activities that are designed to build up their understanding that everyone approaches things differently, and we’ll all get there even if we take different paths. This guy wasn’t allowed to follow his path and do it his own way, and they were unfairly putting him on the spot and forcing him to do it their way.

It’s a rich problem, so I’ll use it again, but I think I’ll set it up and frame it a little differently next time!


Malcolm Swan:

When we’ve done analyses of the results of [our professional development efforts], we’ve found that teachers often move from a transmission approach where they tell the class everything and the students have been fairly passive, they’ve usually moved in two directions.

One is retrograde. They’ve moved towards individual discovery. They say “I’ve been saying everything to these students for so long. What I’ll do now is withdraw and let them play with the ideas. I’ve been saying too much. I’ll withdraw and let them discover stuff.” That’s worse than the place where they started.

The other place is where they move in and they challenge students and work with them on their knowledge together. That’s a better place. That’ smore effective.

And so in professional development, people take a path. Over time they might move from transmission to discovery to collaborative connectionist. So they might actually get worse before they get better.

That’s one of the problems with evaluating whether its been successful by looking at student outcomes. People take awhile to learn new things.

Earlier in the talk, he describes counterproductive designs for professional development:

Most of the time [in teacher professional development] we inform people of something and then we say “go and do it.” That’s not the way people learn. Usually they learn by doing something and then reflecting upon it.

So when you start with a professional development, you say, “Try this out in your classroom. It doesn’t matter if it doesn’t work. Then observe your students and then as a result you might change your beliefs and attitudes.”

You don’t set out by changing beliefs and attitudes. People only change themselves as they reflect on their own experiences.

And then productive ones:

If you’re designing a course, we usually start by recognizing and valuing the context the teacher is working in and trying to get them to explain and explore their existing values, beliefs, and practices.

Then we will provide them with something vividly challenging. It might be through video or it might be through reading something. And this is really different to what they currently do.

And through this challenge we ask them to suspend their belief and try and act in new ways as if they believed differently.

And as they do this we offer support and mentoring as they go back into the classroom to try something out.

And then they come back together again and it’s taken over then by the teachers who reflect on the experiences they’ve had, the implications that come out of their experiences, and recognize and talk about where they’ve changed in their understandings, beliefs, and practices.

What’s great about Malcolm Swan and the Shell Centre is their designs for teacher learning line up exactly with their designs for student learning. It all coheres.

Marbleslides Is Here

Marbleslides is the latest activity from my team at Desmos. It’s simple. We set up some stars. You press a “launch” button and marbles drop.

But here you have collected zero stars. No success.


That’s because your students need to set up parabolic, linear, exponential, sinusoidal, or rational functions to send the marbles on a trip through those stars.



That’s Marbleslides and you and your students should play it this week and let us all know how it goes. If you want a preview, head to LINK and type “eht8”.

If you want to set up your own class, head to the Marbleslides activities listing, choose a function family, and get a classcode of your own.

Here are some quick, below-the-fold notes about what we’re trying to do here and why we’re trying to do it.

Delight. Whenever possible we want students to experience the same sense of delight about math that all of us at Desmos feel. Students can experience that delight both in pure and applied contexts and Marbleslides is that latter experience. Seriously, try not to grin.

Purposeful Practice. Picture two students, both graphing dozens of rational functions. One finds the experience dreary and the other finds it purposeful. The difference is the wrapper around that graphing task. If the wrapper is no more purposeful than a worksheet of graphing tasks, your student may fatigue after the first few graphs. In our Marbleslides classroom tests, we watched students transform the same function dozens of times – stretching it, shrinking it, nudging it up, down, left, and right by tiny amounts. That’s the Marbleslides wrapper. Students have a goal. Their pursuit of that goal will put you in a position to have some interesting conversations about these functions and their transformations.

BTW. Here’s the announcement post on the Desblog.

Great Classroom Action


Scott Keltner sent a drone up in the sky while his students plotted themselves down below. I emailed Scott and asked for his lesson plan and he sent back something involving playing cards and, frankly, none of it made any sense to me and I seriously don’t understand how the downside of cost, time, and effort could possibly outweigh the upside of drones (!) but I’m so curious. Bug Scott via Twitter to write up what he did here.

Julie Reulbach used zombies to create a need for logarithms. Zombies are, obviously, catnip for some students, but that isn’t what caught my eye here. Julie understood that logarithms are a shortcut for inverting an exponential equation. And if you’d like to create a need for a shortcut it’s helpful for students to experience the longcut, however briefly. Watch her work.

Ollie Lovell used one of my unposted tasks with a group of students in Myanmar who spoke very limited English and whose classroom had no electricity. Imagine how your favorite lessons would have to change under those constraints and then read how Ollie changed his. I learned a lot.

Sarah Hagan shares a game from S T called Greed, which helped turn her students’ perception of box-and-whisker plots from useless to useful. Crucially, the game exploits the need for box-and-whisker plots, which is comparison between multiple sets. Creating a box-and-whisker plot for a single set of data will feel pointless, same as teaching someone to use a carrot peeler by using it to paint a house. That’s not what it’s for!

« Prev - Next »