I remember the sweat dripping from my brow as I worked last minute to complete my grant proposal for funds competitively available within my district. With an infant at home, and a full teaching load at the high school, I had almost missed the deadline and my chance.

The grant’s only stipulation was that the funds had to be used to support students within the district, but otherwise, the sky was the limit. My neighboring science teacher took that to heart and was writing a grant for a telescope to aid his students’ discovery of our universe. I sat trying to find the right words to explain why graphing calculators were necessary for my Algebra 1 students. How could I convince self-proclaimed “non-math” types that the tools could potentially open up their mathematical skies just the way a telescope literally could?

Not so far away, some very smart people must have realized the same thing. Enter Desmos, the graphing calculator. I hadn’t yet entered the age of smart-phones. (I am not quite a laggard, but I’m close. I was shamed into getting a smart phone by my 75-year old grandma, who chastised me for not being able to send her pictures of her great-grandkids via my not-so-smart-phone.) But Desmos was different for me. I was impressed from the beginning, and sold on the usefulness from the instant I saw it. What I didn’t know was that Desmos was the cocooned caterpillar, and teacher.desmos.com was the beautiful butterfly about to emerge  My mathematical skies opened up with each Polygraph, Marbleslide, and Activity Builder I explored.

Without a classroom of my own, I found an unsuspecting and eager first-year math teacher and offered to co-teach her class for a day. She thought the offer was too good to be true, and so did I. As we sat and planned how to move from linear to exponential functions, I slyly suggested that we check out Polygraphs. The panic in her face made me think she was stealing school supplies. Not that kind of polygraph, I assured her. Her panic turned to joy when I showed her what Desmos had created.

Here are some of the things we thought of ahead of time:

•  How would we introduce computers into the class? (A cart of Chrome Books would be available, from this point forward, but hadn’t yet been used in the class)
• Did we want students to work in partners or alone? What would be the benefit of either case?
• Did we want students to write anything down?
• What did we want the big mathematical takeaway to be?
• How could we use their responses and actions to move students towards our learning intention?
• How could we use the Polygraph to further our instructional focus on student discourse?

Here’s what we decided:

•  If there were going to be two of us in the room, it could be the perfect time to also learn a new structure for getting out (and putting away) technological resources. We picked a day with longer class periods to try this for the first time.
•  We decided we wanted students to work in pairs the first time, but we wanted to make sure both students were accountable for working. We were hoping this would help with the student discourse piece (see more below).
•  I wanted to go straight for the technology and ditch the paper/pencil, but my co-teacher (the first-year teacher) reminded me that we needed to teach students how to interact with both technology and paper/pencil at the same time. Wise beyond her years is an understatement.
•  We wanted to focus on math practice 6 – attend to precision – with students’ language in discussing slope of lines. We thought this might be particularly helpful when we moved into exponentials.
•  We decided when and where we would stop students and ask them to reflect on the language their classmates were using, the precision of the language, and engage in math practice 3 – critique the reasoning of others.
•  We wanted students talking, arguing, debating…if we want to increase the quality of student discourse we have to begin with some kind of measurable quantity.

And here’s what we found:

• Students quickly came up with a better structure than we had for getting out technology and putting it back. They had been using Chrome Books on and off in other classes for years, and were very willing to help with ideas to make it run smoothly. Notes to self: Students are worthy collaborators. Not only do I need to be willing to listen to their ideas, I need to solicit their thoughts.
• Students working in pairs worked better than we thought. I’m pretty sure that someone in #MTBoS first suggested it, but it worked wonders. Since this time I’ve tried Polygraphs numerous times, and students working in pairs seems to work better every time. Note to self: Students need a chance to try their thoughts out on a partner before committing them to an activity. Give students space to think aloud.
• In hindsight, we didn’t think through enough what we wanted students to write down, and why. We wanted the paper/pencil part to aid the technology part and instead it became just a compliance piece. There are times to use both, in hopes of bridging the gap, but Polygraphs probably isn’t the best one. In this case, I recommend letting the technology speak for itself. Note to self: Never make a worksheet without a clear mathematical purpose. Think twice before printing!
• Starting and stopping students in the midst of Polygraphs was way more complicated than it sounded. The students get hooked quickly, and they don’t like being interrupted. (Would you?) We started saving these conversations for small groups and the flow seem to go much better. When we saw students in between a round, we often popped in for a quick chat to help them reflect on their language and precision. Note to self: Discourse needs to be in service of learning. If it's not, rethink when/how you’re asking for student talk.
• Polygraphs far exceeded our expectations for getting students talking. One of our favorite features is the “What your classmates have asked…” which scrolls through questions other students have asked. These questions spurred students to refine their questions, offer examples when they had none, and became our source for other high-ceiling tasks (Ex: What is the least number of questions you could ask to identify the correct line?) Note to self: Always think through how I can use students’ thinking/work to further their classmate’s thinking/work before I step in and use my thinking/work. Be like Desmos.

 Moral of the story: Skip the sweaty grant-writing and get on board with Desmos Polygraphs!