This isn’t available on the Khan Academy site yet; just YouTube so far. But it responds to my original critique—that nowhere does Khan Academy help students to compare decimals with different numbers of places.

I initially observed that the my feedback was incorporated in an awfully literal fashion. Frank Noschese came to Mr. Khan’s defense:

@Trianglemancsd C’mon, man. Obviously he’s taken your pretty straight forward feedback and very clearly used it in his video. He’s trying.

Maybe Mr. Khan and I can have an extended conversation in New York in September? (Although I am suspicious that he may be telecommuting to that thing!)

I attended E. Paul Goldenberg’s session on Thursday of NCTM in Denver. It was not at all, as advertised, in keeping with the proof strand. But that does not matter.

What matters is this. Goldenberg shared the video below. The whole video is worth your time, but I have queued it up to the 2-minute mark, where a beautiful classroom sequence unfolds (give yourself about 5 minutes for it).

My eyes tear up watching this sequence. I am neither kidding nor exaggerating. It gives me hope for quality classroom instruction in elementary mathematics.

Be sure to notice the transition to a new task at the 4-minute mark, and how the teacher deals with the struggle that occurs at the 6-minute mark.

Also please look in the kids’ eyes. Watch their body language and their waving hands. Watch them think.

Kids are practicing facts in this classroom. The teacher is providing instruction. Contrast with this.

[NOTE: As of 5/2/2013, the video referred to seems to have been removed from YouTube. My apologies. Go search YouTube for "EDI math" and you'll find plenty of examples that are essentially equivalent to the one I refer to below.]

You can flip this latter instructional sequence because it involves telling and choral response.

You cannot flip the first instructional activity because it involves adapting instruction in response to student ideas, and it involves students justifying their thinking to the teacher and to each other.

You can’t flip that.

[NOTE: I have edited some of the comments below in order to focus on the practices that were exemplified in the videos (one of which is now private), rather than on the teachers in them. See my post on norms a while back. My apologies to anyone who feels their words have been altered in ways that do not convey their original meaning.]

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?

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.

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?

Several people have observed that they would love to have audio of the conversations I report under the heading Talking Math with Your Kids. I agree that this would be helpful. But here’s the rub. These conversations are a natural part of our day, and they have to be natural.

My kids have no interest in being show ponies. Oh, they’ll show off for the recording device, but it won’t be natural. Observe Griffin as a young lad in this video, for instance.

He’s totally making faces for the camera and watching himself in the monitor. (You may also note that the spinach is washed; and please forgive the praise style—I know better now!) This mugging behavior has only gotten worse with time.

I do have some ideas for getting good audio, but these will require funds (Do you have a couple thousand dollars for a good cause? Tweet me! We’ll talk!) So in the meantime, we’ll continue the transcribed conversations.

Today’s conversation is a brief one, but I want to make a comparison. The discussion in the following video is not a natural one. (Tip o’ the hat to David Wees for the find.)

Here’s what I mean. The woman discusses cookies because she thinks they will interest the child in question, not because cookies are already under consideration. The question of multiplication (or repeated addition—I have no interest in that distinction here) doesn’t arise naturally either. It arises in the context of putting four chocolate chips on each of three cookies.

To be clear, I have no problem with any of this. But it’s different from the kinds of conversations I am hoping to encourage. The ones I hope to encourage go more like this…

Tabitha (5 years old) and her mother made cookies from one of those frozen-cookie-dough-school-fundraiser things over Thanksgiving weekend. These cookies were stored (unwisely) in a transparent Pyrex container on an open shelf. This led to a desire on Tabitha’s part for a cookie before dinner.

Tabitha: How many cookies can I have? One or two?

Me: Zero. You can have zero cookies.

T: A half?

Me: No. I said zero.

T: Zero whole ones and a half cookie?

Me: Zero halves.

T: And a quarter?

This is a natural conversation about cookies. The opportunity to turn it into a mathematical one was Tabitha asking, How many can I have? I could have played the role of rule enforcer and replied, We don’t eat cookies before dinner; you may have one for dessert. Responding with zero in answer to her question gave her some mathematical wiggle room to play with. And we are far enough along in this talking math adventure that she’s going to play with it nearly every time.