The event was organized by the wonderful folks at The Math Forum. They’ve begun posting video of the talks on their website. I’ve embedded mine below for your viewing and/or heckling pleasure.

Technology and the Curious Mind

Postscript

I wrote a few words about the experience (and posted the slides and manuscript) in a previous blog post.

I gave an Ignite talk (5 minutes, 20 slides, ready-or-not auto-advance every 15 seconds) at this year’s CMC North conference in Asilomar. (Video of the talk is here.) It was quite possibly the most fun I’ve had at any math conference. In the hours leading up to the event, I was more than a little nervous. Then I saw the speaking order:

Gulp.

Just before we went on, one of my co-igniters asked whether it was possible to ruin one’s career in just five minutes. We hoped not. As it turned out, we did alright. In fact, from where I sat, the other nine presenters were all amazing.

To Script or Not To Script

After preparing my slides, I wrote out a script of what I intended to say. I’ve never scripted anything before, but then again I’ve never done anything with such an unforgiving format. I imagined myself falling silent for an entire slide or two. That make-believe mental picture wasn’t pretty, and scripting seemed like the answer. I struggled to get past 80% memorized, so I abandoned the “word for word” approach, didn’t look at my notes at all on Saturday, and made it my goal simply to drive home the main idea of each slide. For anyone who skipped the Ignite talks (shame on you!), or for those who attended but are curious how my live presentation (and occasional bumbling) compared to what I originally had in mind, here are my slides along with what I would have said if I had been able to stay 100% on target.

Slides and Script

Here’s my goal for the next five minutes: To convince you that some of what passes for innovative use of technology in the classroom is actually dehumanizing and therefore destined to be ineffective. And what better way to kick things off than to waste two slides on a blue police box.

For those not addicted to Doctor Who, that’s the TARDIS. An amazing box of infinite potential. It’ll take you anywhere in space, and any time in history. It’s basically a time-machine-powered promise of total freedom.

Here’s another set of boxes with a similar promise. Bigger on the inside? Check. Ability to take you anywhere? Well, sort of. Time travel? Not so much. Anyway, a few years ago one of the box-makers spent billions of dollars developing a shiny new box.

Then they announced that they were going to change the world. In particular? Education. Their game plan? To revolutionize the textbook. Well I watched the seven minute infomercial. And I’m not going to lie. I was stoked. The future looked amazing. And seemed like it was just around the corner.

But then I watched the video a second time. And a third time. The shine wore off. The promise disintegrated into a few gimmicks. “Textbooks got you down? You need some pinch-to-zoom action. And flash cards. And sorting activities where students don’t actually sort anything.”

Needless to say, I was bummed out. “You and me, Apple, we were going to change the world. And all you did was tech-wash the idea that teaching consists mainly of sending the right sequence of letters and images, or in this case, 1s and 0s.”

The problem with this approach is that it treats students as passive. As consumers. Worse than that, it actually trains them to be that way. And what we end up with is more of what we don’t want. Indifference. Apathy. Isolation.

But there’s one part in that video that still resonates with me. They said that if we can stimulate curiosity, we’ve got the spark for learning. Amen to that. But what is it that stimulates curiosity? Digital flash cards? Using a stylus instead of a pen?

Or maybe this: A grid of more than 900 skills begging to be mastered—with on-demand help from Uncle Sal whenever you need it. If you weren’t inspired the first time, just pause, rewind, and play it again. That should do the trick. Did you know you can play YouTube videos at quarter speed? As if normal speed wasn’t painful enough.

I’ve seen one version of our tech-saturated future, and it terrifies me, because it looks like this. All headphones and no heart. Everything that makes us most human just put on pause. This isn’t the revolution I want for my students.

It certainly isn’t what I want for my own kiddos. When they come home from school I want to ask questions like: “What made you curious today? What did you create? What inspired you?”

So here’s what I propose: Let’s use technology in ways that foster—rather than stifle—what is most valuable and most human in us and our students. Here are four ways we can do that. #1, let’s replace indifference…

…with curiosity. Let’s break out our smartphones and capture strange, thought-provoking things we find in the world. In the kitchen, in the checkout line, a dying battery on your phone, or just aimlessly wandering the Internet… Keep your eyes peeled for the things that hook and engage and provoke.

#2, let’s replace consumption with creativity. I have never had a student email me to say “Hey, I just spent a week binge-watching Khan Academy videos. And it was awesome.” But out of the blue, a student of mine did send me this boat he made with an online graphing calculator. He was so proud of what he’d done.

And not because he earned some boat badge. He was stoked because he made something. And making things is awesome. You know paint by number? How about paint-a-minion by equation. All 424 of them!

#3, let’s replace competition with collaboration. I’m less interested in energy points and clicker quizzes, and more excited to see students using things like Google Drive to create and revise and collaborate.

#4… If I ever write my own young adult dystopian novel, it’ll include a scene from a K-12 classroom with 109 students. At one point the hero (an amiable hacker named Eli) will redirect every kid’s browser to student.desmos.com…

In other words, let’s replace isolation with conversation. Headphones and computer cubicles isn’t progress. We need more discourse and more arguments in math class, not less.

If you want to flip the classroom, here’s my model. Let’s flip tech-induced indifference, consumption, competition, and isolation, and replace them with tech-inspired curiosity, creativity, collaboration, and conversation.

In the end, technology is just one tool among many. It’s as powerful or as useless (or worse, as damaging) as we make it. Let’s wield it well. Thank you.

Image Credit

Slide 2, Slide 3, Slides 4-6, Slide 7, Slide 8, Slide 9, Slide 10, Slide 11, Slide 12, Slide 15a, Slide 15b, Slide 16, Slide 17, Slide 18, Slide 19

• We’re a little weak with graphing lines. Some open-ended, Desmos-driven, instant-feedback style practice may help.
• Domain and range? Yeah, not so much.
• Inequalities? Haven’t done them justice. Yet. (Growth mindset, baby!)
• Vertex form for quadratics? Still struggling.
• We tried Des-man a few days before this game and found nothing but pain and frustration. Some could be attributed to me (in particular, a bungled launch of the activity), some to students’ lingering struggles (noted above), and most of the rest to the declining state of our netbook cart. (But they seemed so cool in 2009!)

At any rate, to get that bad taste out of my mouth and set the stage for greater success on the next Des-man go around, I created the Dot Capture Game. Here’s what you need:

• Students (working in pairs)
• Devices (we actually used 50% smartphones, 25% tablets, 25% laptops)
• The world’s greatest, most beautiful graphing calculator

And of course, the handout:

Getting Started

Give a brief intro—or none at all—and turn ’em loose. If your experience is anything like mine, you’ll find yourself the weaving in and out of some great (albeit trivially-inspired) conversations about slope, intercepts, point-slope form, domain, range, inequalities and shading, vertices, direction of opening, etc.

This is definitely not high-quality modeling stuff (it’s not even low-quality modeling stuff), but it proved a great way to engage students with meaningful (read: productive) practice on a variety of topics related to graphing.

Oh, and the winner in my class? Here you go:

Final Thoughts

After trying this out in Algebra 1, I thought I’d throw it at my Algebra 2 and Precalculus students to see what they would do with it. It turned out to be good practice in those settings as well. Before sharing with these followup classes, a quick tweak to the handout was in order. In my first class, several students lost their graphs and expressions after hitting a deadly combination of keys on their device, and only one or two had been keeping a shiny written record. So to protect against future heartache, I added a second page to the handout. Here’s what one of them looked like at the end of class:

Update

Here’s a sweet suggestion from Desmos:

@mjfenton What if Ss rolled two dice to determine which curves they had to use and the numbers also represented the coordinate to capture?

— Desmos.com (@Desmos) May 22, 2014

…and then launched into an algebraic confirmation of that solution.

Now on the one hand, throwing a Desmos-generated graph into a “detailed solutions” handout is a great move because, well, just look at it. It’s beautiful. And hey! Multiple representations! Plus it took about 30 seconds from start to finish. No brainer, right?

Well, on the other hand, including something like that is dangerous, because when you find yourself writing the solutions to questions 6 and 7 (as I did just a few moments later), and these questions ask for a graphical display of the solution to a one-variable linear inequality… Well now you’ve tasted greatness, and you won’t settle for anything else.

There’s just one problem: Desmos doesn’t do linear inequalities in one variable.

Okay, that last sentence is actually not true. Desmos will graph linear inequalities in one variable. You just have to ask nicely. Check it out:

I imagine I’m not the only one to do this (and it would still be pretty cool if Desmos would add one-variable number line graphing functionality… Pretty please?), but I thought I’d share how to do it anyway, just in case anyone is curious (and wants to give one-variable graphing a little Desmos-love).

Here’s How

The best way to explain is to throw a few images in here and let them do the talking. Drop me a line on Twitter (@mjfenton) or in the comments if you have any questions (or tips for how to make this even easier or more awesome). Or if your name is Eli and you have a new feature to announce.

Graph 1

Graph 2

Graph 3

Graph 4

This summer I’m offering a two-day math and technology workshop series for JH and HS teachers. The purpose of the workshop? Equip teachers with digital tools and skills that will help them engage students, promote the CCSSM mathematical practices, and “multiply our hours” as teachers.

The workshop runs twice this summer: June 5-6 and June 23-24.

If you’re going to be in the area (Fresno, CA) this summer, or know someone else who will be, check out the the flyer for more details.

The basic flow for each scenario:

• Set the context (catapult, arrow, ball from roof, etc.)
• Substitute an input, evaluate, explain the result in context
• Substitute an output, solve, explain the result in the context

One student was struggling with the two-solution result to bullet #3 above. “How could there be two answers?”

I’ve been asked this question before, and feel like I’ve been able to help students reasonably well with a combination of questioning, hand-waving, sketching, etc.

But today? I reached into my pocket and added one more element to the conversation:

Now, I love using Desmos on a laptop. Nothing beats that graphing experience in my mind. But to have a functional version of Desmos sitting in my pocket, ready to bring into a conversation at a moment’s notice… That’s cool.