Many videos today, all geared around the learning trajectories of the Math Talk Learning Community (Hufferd-Ackles, et.al).

These "learning trajectories" strike me as positively goofy. The highest level, the ultimate goal, is achieved when the teacher no longer teaches, but "co-learns" and acts on the "periphery". The students are "co-teachers". They decide the shape of the lessons. The teacher no longer teaches.

My "good citizen" survival plan prohibits me from exclaiming, "Good god, what complete horseshit." The plan demands that I express skepticism and disagreement, pose a question that captures the essence of my disagreement, followed by polite dispute of the answer to the question.

I am not temperamentally suited to this mode. I am much happier with "Horseshit!". After all, surely everyone knows why I am skeptically disagreeable, why I dispute the answer to the question, and so on. So why go the long way round?

On the other hand, they haven't booted me out yet, and most of my teachers seem okay with my lengthier approach. I am surprised they don't see the "horseshit" thinking right below the surface, but hey, whatever works.

Anyway. I decide that I've made enough of a fuss yesterday with Amber Hill and Phoenix Park that I just do the doodle routine. (Whenever I want to keep my mouth shut, I start drawing squares in my notebook. My son comes home every week and checks out the number of doodles in the notebook so he can assess how often I was gritting my teeth.)

We watched a video about a teacher "norming" the classroom for "positive interaction". After all, said one of the class leaders, the objective is to help kids understand that making mistakes isn't a disaster, and this teacher (she said) is outstanding at modelling appropriate behavior.

Video:

In what appears to be an second year algebra class, the teacher asks a boy to come up to the front and show his solution for a probability question. He does so, making a minor mistake.

A girl, big hair and bangles, in the back of the class raises her hand and (without waiting to be acknowledged) points out his error. She isn't even slightly rude or gloating--very matter of fact.

The teacher jumps down her throat. "That is not the way we talk in this classroom. I want everyone to have a good attitude."

"I totally have a good attitude!" Bangles protests.

"We don't say 'you're wrong' or 'you made a mistake' here," the teacher declared. "If you disagree with a student's work, you say, 'I have a question' and then ask your question."

"But I don't have a question!"

"Yes, you do. That's how we do things here."

By this time, the boy has figured out his error, erased and corrected it, but the teacher still talks the girl through the whole routine.

I am doodling madly.

"Sam, I have a question about your work. In step 2, you add 3 and 2 and get 7. When I add 3 and 2, I get five. Could you explain your thinking, please?"

"Joe, you found the area of that triangle by multiplying pi by the height. I have a question about that formula, because it's not the one I used. Can we talk about this a bit?"

(In the car the next day, Dudley approved of this technique.

"Kids are afraid of making mistakes. If you take the word 'mistake' away and call it a question, then they won't be as afraid. We want them to understand that mistakes aren't anything to be afraid of. Plus, kids who think someone has made a mistake in error won't be embarrassed if they turn out to be wrong."

"But Dudley, if mistakes are okay, why can't they be called mistakes?"

"Because it hurts kids' feelings."

"But you just said that kids need to understand that mistakes aren't a big deal. How can they learn that if they aren't even allowed to say the word?"

"Well. I just think it's kinder."

"Kinder is ensuring that kids don't gloat, tease, or heckle when pointing out a mistake. That makes sense. But banning the word in order to make kids feel less afraid of the word?"

We arrived at school right about then and never did reach closure.)

Video #2, with discussion first. The students had to solve the problem: 1 divided by 2/3. However, they were not allowed to use an algorithm or method. They had to show their work.

We were split up in groups of 4, and three of the four students at my table--math majors all--did not know how to solve the problem without the algorithm. Thus I, the least math-oriented person in the group, got to explain it.

Explanation, for those who don't know:

How many times does 2/3 go into 1? One time.

How much is left over? 1 - 2/3 is 1/3, which is one half of 2/3.

1 divided by 2/3 is one whole 2/3 and a half of 2/3, or one and a half. Also 1.5 and 3/2.

Try drawing it out if you're still confused.

Anyway. They were somewhat of a Stepford gang, these kids, but they did have a number of interesting explanations for the problem and the solution. One kid even had the algorithm, and the teacher wasn't nice about it. In this world, the only mistake lies in getting the right answer with an unapproved method.

N was in our class today, and she made a comment that really stunned me.

"The answer isn't important. The process is important. You need to impress upon your students the importance of process and the unimportance of the answer."

I doodled with great dedication to detail.