Wednesday, October 26, 2011

Incomplete Manifesto for Growth No. 1

I'm hoping to quote and then comment on each of Bruce Mau's items in his brilliant Incomplete Manifesto for Growth. Sometimes, in order to really absorb something, I just need to copy it down and repeat it to myself. Mau's manifesto is a concrete inspiration both personally and to my pedagogy.

"1.) Allow events to change you. You have to be willing to
grow. Growth is different from something that happens to you. You produce it. You live it. The prerequisites for growth: openness to experience events and the
willingness to be changed by them."

It's difficult to be open to growth. I spend a lot of time trying to keep e/thing the same. Growth is difficult and painful.

Wednesday, October 12, 2011

The Point of Grade 9 Math...

...might not be the math. Just listened to a CBC Ideas broadcast featuring Jean Briggs, an anthropologist, talking about Inuit strategies of child rearing and teaching and, somehow out of that it occurs to me that my focus in Grade 09 math doesn't necessarily have to be the math. It's about learning to learn and about seeing the world differently. It's about the mental equivalent of what a good masseuse might do to your spine in loosening it up and allowing you to move not just more freely, but differently altogether as a result.

Just remembered a connection to the Inuit. According to Briggs, children were often asked things like "Do you (incorrectly) imagine that such and such is the case?" The method is extremely open-ended and non-prescriptive and forces/expects that the child will generate their own response. Prescriptive right and wrong responses are eschewed.

Also, according to Briggs, some variation of counter-factuals are used. An answer might be given that is intentionally wrong with the expectation that the child will know it is wrong and deduce the "correct" and opposite answer.

Imagine if, in my math class, I said to one side of the room "For this class, I want you to only give me wrong answers." And, at the same time I tried to lead/push/divert them into productively wrong answers. Maybe I could (a) make them less afraid to be wrong and (b) get some good insights out of it.

I wonder how some of my super-keen kids would take to this?

Tuesday, April 27, 2010

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.

Monday, February 22, 2010

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.

Saturday, January 23, 2010

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.

Friday, December 4, 2009


The day before yesterday one of my less engaged students (in a class full of students who find it difficult to stay engaged) had her head down on the desk. I told her to wake up and she replied, head still down on the desk, that she was awake. And so, predictably for all concerned, I told her to lift her head off the desk and that no one's allowed to have their head down in my class. (As if they were allowed to do it in other classes, anyway. But that's beside the point.) When she lifted her head up she had this extremely put-upon, angry expression on her face. If you're a teacher you've seen it. It's the why do I have to be here and why are you making me do this shit? face.

In the car on the way in to school this morning I connected this to something that I heard Pema Chodron say in an interview with Bill Moyers. She was quoting some Buddhist luminary or other. It was something to the effect that we hate our suffering but are in love with what causes it. So the alcoholic hates the hangovers, or the embarassment, or the way he fails his kids but loves drunkenness or the booze itself. And this student who was hating being there and who could barely restrain herself from lashing out was really suffering. She just hated her situation and wished that it would change or be different. But that wasn't going to and couldn't just happen. What is she in love with that causes her suffering that she can't and won't change?

In part, she's in love with not understanding that it's her responsibility to change things. She just wants it to change. She doesn't want to do the work to be in school but she still lets herself be stuck in school. In cruder, less empathetic terms, she needs to shit or get off the pot. That's what most of us need when we're stuck. We're stuck because in some sense we're unwilling to do one or the other. But it's more, too. She could change herself. It wouldn't be easy. Ultimately, it's the project of a lifetime (enlightenment). But that's a path she could take. She could find a way not to suffer in this situation.

Perhaps she's in love with not changing herself. Perhaps she's in love with being a child and therefore with not being responsible for herself. As am I. As are most of us.

Tuesday, August 18, 2009

Identifying Strengths and Weaknesses

Good teachers focus in on particular strengths and weaknesses and are able to say what category these strengths and weaknesses fall into.