How Many Squares?


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I had dinner with the kiddos at Round Table tonight. (Side note: yum.) Must’ve had squares on the brain (thanks Dan and Anna!) because as soon as I sat down with the receipt I folded (and unfolded) it like this: And then I asked Ainsley (4): “How many squares do you see?” She counted the top row: “1… 2… 3… 4…” Then a long pause, followed …

Beyond Explaining, Beyond Engaging

In my first few years in the classroom, I held the notion that the best way to improve as a teacher was to hone my explaining skills. I figured that if I could explain things more clearly, then my students would learn more. It only took me a few years to realize that this philosophy of personal development was woefully incomplete. (Quick learner, …

Pedagogy and Content Knowledge, Part 2

Yesterday I asked which is more important for a math teacher: teaching ability or content knowledge. Several commenters reframed the question as pedagogy vs content knowledge. I found that shift helpful, so let’s run with that. My original plan was to highlight a few comments here, and then offer a twist (or two) on the original question. But the post received way more …

Teaching Ability and Content Knowledge

Last weekend my wife and I had the privilege of sharing a meal with Scott Miller, David Sladkey, and each of their wives. Awesome food, excellent conversation. It was the highlight of a great weekend at the DuPage Valley Math Conference. At one point, David asked an intriguing question that sparked a lengthy discussion. I’ll share the question here in the selfish hope that I’ll be able to …

Some Thoughts on Modeling

Here’s a definition of modeling I’ve offered in a couple of conference sessions: Describing the world with mathematics, in order to make reasoned predictions and decisions. That I borrow heavily from Dan Meyer is readily apparent, especially when considering some of the activities I’ve created over the last couple of years (e.g., Charge!, LEGO Prices, Predicting Movie Ticket Prices, Mocha Modeling). …

Charge! v2 – Activity Makeover


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Background. I’ll share an activity. Offer some ideas on what’s wrong. Invite you to share your own diagnosis/treatment. Then (end of week) share an upgraded version of the activity. (More details about this series are available here.) Several Mondays ago, I shared the Desmos Activity Builder version of Charge!, a linear modeling task where students predict how long it will take for a …


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LEGO Prices vs Marriage Age – Contrasting Activities


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I spend a fair amount of my time at Desmos creating activities with the Activity Builder. In my mind, the job becomes more and more interesting over time for at least two key reasons: Over time, the toolset expands. Over time, our sense of how to use the toolset expands. That is, our pedagogy improves. These two developments play off one another, and we find ourselves with more and …

CMC North 2016

Math teachers are amazing. Exhibit A: Last weekend I spent an hour with a group of math teachers who woke up early on a Saturday morning to hone their craft. We were just steps away from the beach in Monterey, and yet they’re willing—hungry, even—to gather in a room to reflect on their own learning and teaching, even at 8 am. That’s just awesome. Snapshot …

Parallel Lines – Activity Makeover Series


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Background. I’ll share an activity. Offer some ideas on what’s wrong. Invite you to share your own diagnosis/treatment. Then (end of week) share an upgraded version of the activity. (More details about this series are available here.) Activity and Diagnosis Some months back, I wrote an activity called Parallel Lines. Here’s the description: “In this activity, students explore connections between the graphs and equations of …

Diagnosis and Treatment – Activity Makeover Series

Last week I gave a talk at CMC South called Principles for Building and Using Effective Digital Tasks. For the “building” piece, I shared five principles from the Desmos Activity Building Code. For each principle, I offered an exemplar activity. In one case, I even offered an anti-exemplar. I find these contrasts between what works and what doesn’t particularly helpful for developing my own capacity to build …

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