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.

Suffering

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.

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.

Due Dates and the Clarity of Expectations

BTT1O were to hand in their summatives today. I'd told myself to be ready for some students not to be done. I was trying to psych myself up to be a tough guy about it. I was not prepared for almost everyone not to be done. This included a couple of my star students.

On reflection, I did not lay out the tough guy, hard ass expectations all that clearly up front and I have, in general, not done a clear and explicit job of handling due dates. (Which are a mess in the Ontario system, now.) In fact, I need to generally do a better job of being explicit in my expectations with both BTT1O and ICS3M.

I thought that the expectations in terms of what to hand in were well laid out in the summative assignment this time around. I got that part right. But I should have spoken to the importance of meeting the deadline and that the deadline was the beginning of the class.

Attention, Attention

We're fully in summative mode in ICS3M. E/one is working on it in class. One thing that all levels of the summative can use (as a bonus) is the ability to write text to files. So, I spent about 10 mins in class today going over how to do this. What surprised me was the number of students who didn't even bother to pay attention and this was even though I'd told then that it would only take about 10 minutes and that they would need this if they were to go for the bonuse marks on any of the summative levels.

What is perplexing me about this? That it is so clearly in their interest to listen so that they know how to do it and that they aren't? Is it the case that it's not clear to them that it's in their interest?

I'm inclined to think that they are assuming that they don't need to listen now. That they'll be able to get this info from me later when the information will be immediately useful. If I thought this behaviour just came under the heading of general rudeness, that would be one thing. But one student that I particularly singled out for not listening was quite open and nice with me afterwards. It's not intentional rudeness however much it might incidentally be rude.

Perhaps it's the internet generation (Gen I) thing. They're used to information on demand so they just assume that that's how it will be with what I was giving them today.

Alfie Kohn on reform and a Secretary of Education

Kohn, who is surely one of the most interesting and provocative educational theorists out there today, talks about who Obama should choose for Secretary of Education in the U.S. Along the way, he speculates that much of what passes for school reform is actually a retrenchment of the status quo - stateside, at least. Since what happens there often shows up here as at least an influence, I present it for your delectation.

Understanding Student Ability

Today at Incredibly Amazing HS, all the Grade 9 Applied teachers gathered together to discuss the students each felt were at risk academically.

In the first place, that's a cool thing that teachers were given the time during a regular day to meet and figure out who was at risk. Certainly, nothing like that happened at my previous school even though that school had a reputation (deserved, I think) as a good school. There's an unusually strong focus here on identifying kids who are at risk of failing and taking steps to keep that from happening.

But what I want to reflect on here is that the real bonus for me as a newbie teacher was the opportunity to see how other teachers - particularly more experienced ones - understood the strengths and weaknesses of students. I had a couple of "Aha" moments (at least) in which I listened to a teacher's take on an at-risk student and went to myself "Yes I should be looking at that aspect of a student's performance." Or that I should understand this aspect of learning in this or that particular light.

Categories of Strength/Weakness

Abstraction - How difficult is it for the student to deal with abstract material?
One on One Attention - Does the student need an above average of one on one attention in order to understand what's going on?
Organization - an obvious one but particularly important for weaker students who don't need the extra challenge of trying to track miscellaneous bits of information and paper. Kids with organizational difficulties are obvious candidates for a learning strategies mini-course that Incredibly Amazing HS is going to run after Christmas.
Tolerance of routine change - Lots of kids are really sensitive to changes in their routine at school and at home. Sometimes they need to be able to chill out when they get hit with a change. It helps if you know a kid's in this category.
Information retention - how long can the student retain information that they've studied? Obviously, if this is aproblem for them, exams will be a challenge. The eye opener for me with this one was to conceive of a student's exam performance as being a function of the amount of time for which they could retain the information. It's productive to look at it in this light.