Skills practice [#NCTMDenver]

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.]

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Course design question

Brian Frank observes:

Lots of physics majors get by with strong algebra skills.

Same story in Calculus, of course. And you can substitute “calculator” for “algebra” to describe a whole mess of other math courses.

Shouldn’t we be ashamed of ourselves when we see this happening? Shouldn’t we be designing courses (and course sequences) in which this is not possible? Isn’t it time we (as a field) stopped living by last century’s textbooks, allowing students to skate by on last century’s skills?

Should we be designing courses that require critical thinking; courses that require students to really, deeply learn the material?

I know Brian’s working on that problem. Shouldn’t more of us be reading his work and taking his example?