Good turn out for my session Saturday morning (EIGHT O’CLOCK!).

Alternate title: “Slaughtering Sacred Cows w/ Your Host, Prof. @trianglemancsd.” #NCTMDenver

— Dan Meyer (@ddmeyer) April 20, 2013

Rate of change & accumulation – BIG ideas for Middle School and beyond. @trianglemancsd #NCTMdenver

— Marc Garneau (@314Piman) April 20, 2013

We’re taking simplifying radicals, rationalizing denominators, factoring, cubics, quartics, & functions to the woodshed here. #NCTMDenver

— Dan Meyer (@ddmeyer) April 20, 2013

@trianglemancsd emphasizing experiencing ideas in informal contexts as a foundation for higher, formal math. RME everywhere! #NCTMDenver

— Raymond Johnson (@MathEdnet) April 20, 2013

Haven’t thought about rates of change, derivatives, etc in a long time. @trianglemancsd stretching my brain this morning!

— Katherine Bryant (@MathSciEditor) April 20, 2013

I’ll get some more details up here sometime soon. In the meantime, here’s the handout (.pdf). And here’s the slide deck (.zip, and which—to be honest—was just a photo album on the iPad; the simplicity of this was liberating).

Here are Alison Krasnow’s notes from the session.

One last thing…this is the absolute best form of session feedback, as far as I am concerned—getting to read someone else’s notes on the session speaks volumes about what participants experienced (in contrast sometimes to what I think we did).

The slides:

**UPDATE**: This talk has been adapted to a paper submitted to *Mathematics Teaching in the Middle School*. I’ll keep you posted on its progress.

My favorite way to share a talk ever. Although I would have watched the video.

Thanks for highlighting your recent session. I was working with a group of HS teachers recently who are preparing for a new common core course for 9th graders. In it students are asked to interpret the average rate of change of a function over a specified interval. This is new territory for teachers and students, so your work here provides insight into the informal exploration of these ideas. Do you have plans to add commentary to the slides?

I think we’re looking at confronting some misconceptions held by teachers and students. I remember coaching an Algebra I teacher during a transition from linear to quadratic equations. Students were looking a graph of each when one asked, “So does this parabola have a slope?” This question was promptly answered and the discussion ended.

As soon as we hit graphs, we lose all sense of context; discussions revolve around rise/run, and we no longer ask the question: How is one quantity changing with respect to another?

I’m sure one challenge is that many teachers who teach middle school or entry level HS math don’t have a solid understanding of the enduring ideas of Calculus. I appreciate the reorienting you’ve initiated here.

Hey Christopher, I actually recorded the audio for your session on my computer. Do you want it?

I do!🙂

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