A Great Discussion and a lot of Abbreviations

First: honors physics had the best discussion today.  We went through some graphs, practicing whether they told us about a CVPM (constant v) motion, a CAPM (constant a) motion, or neither.  It's pretty early practice in our CAPM unit, so we're just learning the ropes of what each graph says about the motion.  This was our set of graphs (thanks to Minds On Physics and Kelly O'Shea):

We've done some modeling of carts on ramps, finding functions for the final velocity as a function of delta t and seeing the shape of x vs t), so that was their background with accelerated motion (that, and the curve in our error analysis of... well, I'll save that post for another day).  Everything was smooth sailing until one unlucky soul got graph H. 

After a bit of fumbling to an answer, I opened it up.  They were all opened up for questions, but this was the one the everyone was unsure of.  After a few minutes of half answers followed by examining of my face for feedback (that wasn't forthcoming), they really engaged with each other.  Discussions are really easy to have between each kid individually and the teacher, but it's difficult to get them to discuss with each other, particularly when the topic's not subjective.  The biggest key is for me to shut up.  It's hard to do, but a little patience will see them start to really turn their brains on. There's a correct answer here, but what is it?  The tipping point here is when they start actually listening to each other - you know you're there when they analyze the consequences of someone else's argument, and it's a beautiful thing.

     But isn't it easier if I just confirm/deny their answers, and let everyone know what the correct response is?

It depends on what you mean by easier.  Easier for me? Yes. Quicker? Yes. More comfortable for them? Yes.  Better for them to learn how to reason through an unfamiliar situation? No.  Better for them to build a mental model of the process?  Not even close.

Atul Gawande (I'm linking to John Burk here, because that's where I heard of him) has this thing about stages that learners go through: he identifies them as Unconscious Incompetence, Conscious Incompetence, Conscious Competence, and Unconscious Competence (there's a great scene from Waiting for Guffman on this topic...).  I'd sum those up as:

UI: Clueless - doesn't know what the game is

CI: Knows the game, can't play it well

CC: Can do it, but have to think about it

UC: No sweat - like second-nature

The trick about this progression (well, there are two, but the second one I'm saving for another day!) is the frustration and self-confidence swings during this journey.  I made this graph to sum it up:

 

• The understanding increases as you move from level to level, but you'll always have plateaus that you'll have to break through.
• Your confidence really takes a hit as you figure out what you don't know (conscious incompetence), rebounds, and then goes off the charts as you really figure it out.  This is one way to get a handle on where you are on the chart: if you have apprehension, you're not at UC (but you might be at UI!)
• The frustration of going from unconscious incompetence to conscious incompetence can be brutal.  You have started to learn how little you know, and the hill can seem steep.  This, however, is the only way through to competence of any sort.  Ignoring this (by having passive study or avoidance) does not fix the problem.  There's some frustration in clearing the last hurdle, but much less, because your confidence is bolstered by having competence in the material already.

There's a connection that I make here to that study (which I still can't find) about preparing for an exam by passive study or a period of time, cramming, and taking a test.  The test-takers were best prepared (now they really know what they do and don't know), but least confident. That confidence can be a bit of false internal feedback.  You have to be aware of it, push through it, and know that good times are on the other side. 

I see a lot of skills that should be UC for students (like algebra, graphing, writing) take the forefront as points of difficulty; maybe they studied to become consciously competent for a test a few years ago, but that's not enough when you're trying to build on those skills.  You need to be able to do them without thought or hesitation - you need to be unconsciously competent.