Technology whenever!

I like technology. I like the web. I like computers. But as a math teacher I'm on the blackboard all the time. When I read about all the cool stuff that other teachers are doing, I get jealous. So why don't I book some lab time and do it?

The answer is in the last sentence. I have to book lab time and that's not a trivial exercise since the horizon for available time is something like a couple of weeks. I'm a new teacher. I really don't know exactly where I'm going to be in two weeks. Plus that's not the way I work with technology. I want my technology here and now when I think of it and as I think of it. I need to be able to use it spontaneously because using technology is about creativity and I need spontaneity for that.

Until I'm in a wired classroom, I think it's the board for me. I can improvise on the board.

Figuring Things Out

About 20 minutes into a really interesting talk on Information Overload at the Web2.0 conference in New York this year (I think) Clay Shirky says something that is simultaneously so basic and so insightful about teaching that I had to put it down somewhere:

"...we've known the formula for hydrochloric acid for some time now. We're not asking the students to figure it out because we need to know it. We're asking them to figure it out because we need them to have experience figuring things out." (via BoingBoing)

It's so easy to lose sight of the fact that this is one of the, if not the fundamental goals of education. They need to have experience figuring things out.

Long after they've forgotten their last piece of trigonometry, knowing how to figure things out will be the thing that keeps carrying them forward in life.

The question is how I should conduct my practice in light of this. Clearly, I want to emphasize this attitude in class. And I want to give them lots of opportunities to figure things out. And I want to demand that they figure things out. i.e. I need to expect it of them. And I want to model figuring things out. The implication of this last thing is that I need to not have everything figured out when I go into class. They need to see me do it.

Cognitive Load

Gary Davis at Republic of Mathematics (which is starting to look like a v. interesting read from the POV of mathematics education) refers to an interesting concept (apparently originating with John Sweller). The notion is "cognitive load" and it deals with the idea that some concepts or operations just require so much cognitive processing that most or many students get stumped by them. The key point here is that teachers should keep the cognitve load in mind when teaching and actively try to manage it.

The example he gives is of students trying to expand -3y^2(4y^3 - 6y + 7). It's one thing to get them to expand something like y^2(4y^3 - 6y + 7) but throw in a coefficient of 3 - not to mention a minus sign and it's just too much to process. But if we're thinking about the "cognitive load" then we can break it down into smaller chunks. First you could multiply through by the y^2 to get -3(4y^5 - 6y^3 +7y^2). Then you could "bring in" the 3 to get -(12y^5 - 18y^3 + 21y^2) and finally bring in the minus sign, switching the signs of every element within the brackets to give -12y^5 + 18y^3 -21y^2.

Many or most teachers would do this anyways but I think I too frequently overlook this and, for everyone, I think the notion of managing the cognitive load is a useful one.