Tag Archives: nctm

A short talk I gave this spring

The constraints are these: Five minutes, 20 slides. They advance every 15 seconds whether you are ready or not.

Here is my first stab at the genre, from this spring’s NCTM/NCSM conference in New Orleans. The others who presented that day are all worth watching. You can get the complete list, links and a bit more context from The Math Forum, which hosted the talks.

Enjoy.

The hexagons are here! [#nctmnola]

Forgive the delay. Here are pdf files of the hexagons we built for use in my hierarchy of hexagons lessons. You should be able to open and edit them in Adobe Illustrator. Consider them CC-BY-SA.

Set 1 (pdf)

Set 2 (pdf)

Shout out to former students Jen Carlson, Nadaa Hassan and Brenna Magnuson for collaborating on these.
Creative Commons License
Hexagons by Christopher Danielson is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

Update: Below is the current complete set, with added hexagons from former students Ruth Pieper, Brandon Schwab and Mona Yusuf.

hexagons.complete.set

What WAS that? or, What was THAT? [#NCTMDenver]

We watched this video during the closing session in Denver.

I love this video. I find it amusing and clever. The moment where Vi Hart folded the guacamole into the interior of the hexaflexamexagon was marked by an audible gasp of delight in the room.

But…

Somebody needs to explain to me what this is. Is it a lesson? Is it a tasty bite-sized morsel of entertainment? Is it an inspiring call to mathematical action?

Seriously.

Because Vi Hart works for Khan Academy.

Khan Academy is a school (at least metaphorically, but we have reason to believe that Khan and Gates see it more literally than that). So is this an assembly in the auditorium?

simpsons.yo.yo

It turns out that Hart thinks it’s a lesson. Lessons have objectives. Can you guess hers? She began a sentence this way, “The main educational purpose [of this video] is…”

Watch the video again if you need to. Then you may scroll down for the answer, which will be in the comments.

We also watched Hart’s “i” video.

She said, “Technically, it was a bad video because I lost subscribers [on YouTube]. But numbers don’t matter.”

She cringed at her own words and observed that saying numbers don’t matter in a ballroom full of math teachers is probably a bad idea. I think we all understood that she meant to say that popularity is different from quality, and is a direct indicator of neither quality nor effectiveness. It is in this spirit that her numbers don’t matter quip is strange.

Has anyone from Khan Academy ever given a talk which did not use the number of views, or hits, or followers, or lessons served?

She and her father (George Hart) had already exchanged the number of views of each of their first viral videos. Number of views as a measure was discussed on at least five separate occasions during the hour including the introduction by Outgoing Past President Michael Shaughnessy (whose title I am absolutely not making up, and which is strangely not redundant).

Which brings me back to my original question. What was that? What was that video, exactly? What was that talk? Anyone?

The goods [#NCTMDenver]

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

Thanks to Ashli Black (@Mythagon) for the shot of title screen.

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.

road.to.calculusOne 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.

Where do questions come from, part 2

In part 1 of this discussion, Dan Meyer gave his take on where questions in math class come from, or should come from. Dan’s position could be summarized this way: Everybody in my class can’t be working on their own question; I can’t manage that. At the same time, I don’t want to force questions down students’ throats because I use up a lot of my authority doing so. So I want to create classroom situations in which the questions we are answering seem as natural as possible to students. 

Here in part 2, Karim responds to the same question, having heard Dan’s thoughts. He points to an important difference between Dan’s work and his own. In a Mathalicious lesson, the questions are written down on a handout. In a Dan Meyer 3 Act lesson, the questions arise from the class’s experience with a video or photograph; the questions are not fixed in writing.

But neither are the questions especially open. Recall that Dan said in part 1, “I get that at some point the teacher’s going to have to say, This is what we’re going to do today.”

So maybe an important difference between these two isn’t so much where the questions come from (although you’ll soon see that Karim thinks about this very differently from Dan), as it is where they appear to students to have come from. In both cases, questions come from the lesson’s author. Dan is very concerned with student investment in this question-with whether students see the question as the natural one to ask. Karim seems less concerned with this latter issue.

Karim: So if you look at a Mathalicious handout; for example, how many color combinations are there available on Nike ID? And at what point does that cause paralysis by analysis? Or the health insurance one. That’s not something that can at all be encapsulatable in a single piece of multimedia.

And so therefore, we have to lay this narrative. But when we do it, if you look at the handouts, there are very few periods. They’re almost all questions. Every question is a legitimate question.

[We ask] So what do you think…if the insurance company has to charge the same price, how much are they gonna charge? And what do you think is gonna happen next?

And, yeah, like there’s gonna be an answer to that. But the question is a sincere one.

And so then the question is where does that question come from? Because that clearly is a bit more kind of paternalistic than Here’s a piece of multimedia, let’s as a class, let’s talk about what the questions are and then for the sake of efficacy let’s decide on one, but that one kind of came from you guys, kind of the democracy of you.

Mathalicious lessons are quite different from that. So where do those questions come from? I don’t know. I don’t know how to answer this. You know our goal is to be Socratic, and so where did Socrates’s questions come from?

And I don’t know how to answer that without just coming back to this idea of art. You know? Where did the Ninth come from? I really believe that if you ask Beethoven where the Ninth came from, I think he would say, The Ninth existed; my job was to conduct the Ninth. And I mean conduct as in I am a conduit for the Ninth. 

Christopher: In a Platonistic sense.

Karim: Yeah. The Ninth was out there and it’s this sublime piece of music. The Ninth was out there and it was just waiting for somebody to hear it and write it down. And similarly I do think that there are just questions that are really interesting. These questions want to be asked. And so…who’s asking that? I have no idea.

But I can tell you that, as someone who has spent years writing these scripts, I can tell you when a question feels forced and I can tell you when a question feels like it’s flowing. And when it feels like it’s flowing, it does not feel like it’s flowing from me.